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Hardest problem I ever seen

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I have no idea my brain is not smart enough to do this. Whoever solves this is truly a genius!!!!!

A site is any point (x, y) in the plane such that x and y are both positive integers less than or equal to 20.

Initially, each of $$400$$ the sites is unoccupied. Amy and Ben take turns placing stones with Amy going first. On her turn, Amy places a new red stone on an unoccupied site such that the distance between any two sites occupied by red stones is not equal to$$\sqrt{5}$$. On his turn, Ben places a new blue stone on an unoccupied site. (A site occupied by a blue stone is allowed to be at any distance from any other occupied site.) They stop as soon as a player cannot place a stone.

Find the greatest $$K$$ such that Amy can ensure that she places at least $$K$$ red stones, no matter how Ben places his blue stones

Feb 20, 2019
edited by CalculatorUser  Feb 20, 2019

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See the solution here: https://artofproblemsolving.com/wiki/index.php?title=2018_IMO_Problems/Problem_4

Feb 20, 2019